Question

Determine higher order derivatives requiring the chain rule Question Given h(x)=cos(6x-2), find the second derivative, h''(x). Do not include "h''(x)"

Answer 1

To find the second derivative of h(x)=cos(6x-2), differentiate h(x) twice and simplify the expression.

Step-by-step explanation:

To find the second derivative, we need to apply the chain rule twice. The chain rule states that if we have a function f(g(x)), the derivative is given by f'(g(x)) * g'(x). For the function h(x) = cos(6x - 2), the derivative is h'(x) = -6 sin(6x - 2). To find the second derivative, we need to differentiate again:

1. Differentiate the function -6 sin(6x - 2) using the chain rule: -6 * cos(6x - 2) * (6).
2. Simplify the expression to get the second derivative: -36 cos(6x - 2).

Therefore, the second derivative of h(x) is -36 cos(6x - 2).